(For item (H) you need Peter Paule
and Markus
Schorn's Mathematica
implementation of the Gosper and Zeilberger algorithms which are
available directly via
the WEB or via e-mail request to peter.paule at risc dot uni-linz dot ac dot at.
You will also want to get
Marko
Petkovsek's (Marko.Petkovsek at fmf dot uni-lj dot si)
Mathematica program Hyper which
finds all "hypergeometric term" solutions of a linear recurrence with
polynomial coefficients.)

The package comes with complete documentation, a tutorial, and an installation guide.
They should work with any version of
Mathematica, except that Gosper's and Zeilberger's
algorithms require Version 2.0 at least.

(For item (H) you need Peter Paule
and Axel
Riese's Mathematica
implementation of the q-Gosper and q-Zeilberger algorithms which are
(soon) available directly via
the WEB or via e-mail request to peter.paule at risc dot uni-linz dot ac dot at.
You will also want to get
Marko
Petkovsek's (Marko.Petkovsek at fmf dot uni-lj dot si)
Mathematica program q-Hyper which
finds all "q-hypergeometric term" solutions of a q-difference
equation with rational coefficients.)

The package comes with complete documentation, a tutorial, and an installation guide.
They should work with any version of
Mathematica, except that the q-Gosper and q-Zeilberger
algorithms require Version 2.0 at least.